Download - Limites trigonometricos
![Page 1: Limites trigonometricos](https://reader036.vdocumento.com/reader036/viewer/2022083022/58aa71c81a28abbc1e8b4ff1/html5/thumbnails/1.jpg)
32)
limx→0
sen4 x2 x
=¿ sen 4(0)2(0)
=¿ (0)(0)→Indeterminado
limx→0
sen 4 x4 x
.4 x
2 x=
limx→0 ( sen4 x
4 x.4 x )
limx→0
2x = (
limx→0
sen4 x
4 x ). limx→0
(4 x )
limx→0
2 x =
(1 ) limx→0
(4 x )
limx→0
2 x = limx→0 ( 4 x
2 x )
= limx→02 = 2 Respuesta
33)
limx→0
sen2x12x =
sen2(0)
12(0) = sen0
0 = 00 →Indeterminado
limx→0
sen2 x2x
.2x
12x
= limx→0 ( sen2 x
2 x.2x)
limx→0
1
2x
= ( limx→ 0
sen2 x
2 x ). limx→ 0
(2 x )
limx→0
1
2 x
= (1 ) lim
x→0(2x )
limx→0
1
2 x =
limx→0 ( 2 x
12x ) = lim
x→0(4 ) = 4 Respuesta
34) limx→0
tan x2 x = tan 0
2(0)=¿ 0
0→indeterminada
![Page 2: Limites trigonometricos](https://reader036.vdocumento.com/reader036/viewer/2022083022/58aa71c81a28abbc1e8b4ff1/html5/thumbnails/2.jpg)
limx→0
sen xcos x2x
= limx→0
sen x2 xcos x = lim
x→0
sen xx. x
2 xcos x =
= limx→ 0 ( sen xx . x)limx→0
2xcos x=
limx→ 0 ( sen xx )( lim
x→0x)
( limx→0
2 x)( limx→0
cos x ) =
( limx→0
x)
( limx→0
2 x) =
= limx→ 0
x2 x = lim 1
2x→0
= ½ Respuesta
35) limx→0
3 x2
6 sen2 x= 3(0)2
6 sen20 = 00→indeterminacion
limx→0
3 x2
6 sen2 x=limx→0
3 x2
6 sen x . sen x=
limx→0
3 x2
6 sen xx. x sen x
x. x=
limx→ 0
(3 x2 )
limx→0 (6 sen xx . x sen x
x. x) =
limx→0
(3 x2 )
limx→0 (6 sen xx . x) lim
x→0 (6 sen xx . x) =
limx→ 0
(3 x2 )
( limx→ 06)( lim
x→0sen x
x ) (limx→0x )( lim
x→0sen x
x )( limx→0x )
= limx→0
(3 x2 )
limx→ 0
(6 ) ( limx→0x) (limx→ 0
x )=
limx→0
(3 x2 )
limx→0
(6 )(limx→0x2)
=
6 limx→0
(3 x2 )
( limx→ 0x2) =
6 limx→0
(3 x2 )
x2 = 6 (3) = 18 Respuesta